posic/talks/dpg_2008.tex

   1 \pdfoutput=0
   2 \documentclass[landscape,semhelv]{seminar}
   3
   4 \usepackage{verbatim}
   5 \usepackage[german]{babel}
   6 \usepackage[latin1]{inputenc}
   7 \usepackage[T1]{fontenc}
   8 \usepackage{amsmath}
   9 \usepackage{ae}
  10
  11 \usepackage{calc}               % Simple computations with LaTeX variables
  12 \usepackage{caption}            % Improved captions
  13 \usepackage{fancybox}           % To have several backgrounds
  14
  15 \usepackage{fancyhdr}           % Headers and footers definitions
  16 \usepackage{fancyvrb}           % Fancy verbatim environments
  17 \usepackage{pstricks}           % PSTricks with the standard color package
  18
  19 \usepackage{pstricks}
  20 \usepackage{pst-node}
  21
  22 \usepackage{graphicx}
  23 \graphicspath{{../img/}}
  24
  25 \usepackage{semcolor}
  26 \usepackage{semlayer}           % Seminar overlays
  27 \usepackage{slidesec}           % Seminar sections and list of slides
  28
  29 \input{seminar.bug}             % Official bugs corrections
  30 \input{seminar.bg2}             % Unofficial bugs corrections
  31
  32 \articlemag{1}
  33
  34 \special{landscape}
  35
  36 \begin{document}
  37
  38 \extraslideheight{10in}
  39 \slideframe{none}
  40
  41 \pagestyle{empty}
  42
  43 % specify width and height
  44 \slidewidth 27.7cm
  45 \slideheight 19.1cm
  46
  47 % shift it into visual area properly
  48 \def\slideleftmargin{3.3cm}
  49 \def\slidetopmargin{0.6cm}
  50
  51 \newcommand{\ham}{\mathcal{H}}
  52 \newcommand{\pot}{\mathcal{V}}
  53 \newcommand{\foo}{\mathcal{U}}
  54 \newcommand{\vir}{\mathcal{W}}
  55
  56 % itemize level ii
  57 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
  58
  59 % topic
  60
  61 \begin{slide}
  62 \begin{center}
  63
  64  \vspace{16pt}
  65
  66  {\LARGE\bf
  67   Molecular dynamics simulation study\\
  68   of the silicon carbide precipitation process
  69  }
  70
  71  \vspace{24pt}
  72
  73  \textsc{\small \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
  74          K. Nordlund$^2$, B. Stritzker$^1$}\\
  75
  76  \vspace{32pt}
  77
  78  \begin{minipage}{2.0cm}
  79   \begin{center}
  80   \includegraphics[height=1.6cm]{uni-logo.eps}
  81   \end{center}
  82  \end{minipage}
  83  \begin{minipage}{8.0cm}
  84   \begin{center}
  85    {\footnotesize
  86     $^1$ Experimentalphysik IV, Institut f"ur Physik,\\
  87          Universit"at Augsburg, Universit"atsstr. 1,\\
  88          D-86135 Augsburg, Germany
  89    }
  90   \end{center}
  91  \end{minipage}
  92  \begin{minipage}{2.3cm}
  93   \begin{center}
  94   \includegraphics[height=1.5cm]{Lehrstuhl-Logo.eps}
  95   \end{center}
  96  \end{minipage}
  97
  98  \vspace{16pt}
  99
 100  \begin{minipage}{4.0cm}
 101   \begin{center}
 102   \includegraphics[height=1.6cm]{logo_eng.eps}
 103   \end{center}
 104  \end{minipage}
 105  \begin{minipage}{8.0cm}
 106   \begin{center}
 107   {\footnotesize
 108    $^2$ Accelerator Laboratory, Department of Physical Sciences,\\
 109    University of Helsinki, Pietari Kalmink. 2,\\
 110    00014 Helsinki, Finland
 111   }
 112   \end{center}
 113  \end{minipage}
 114 \end{center}
 115 \end{slide}
 116
 117 % contents
 118
 119 \begin{slide}
 120
 121  \begin{center}
 122  {\bf
 123   Molecular dynamics simulation study\\
 124   of the silicon carbide precipitation process
 125  }
 126  \end{center}
 127
 128  \vspace{16pt}
 129
 130  {\large\bf
 131   Outline
 132  }
 133
 134  \vspace{16pt}
 135
 136  \begin{itemize}
 137   \item Motivation / Introduction
 138   \item Molecular dynamics simulation details
 139         \begin{itemize}
 140          \item Integrator, potential, ensemble control
 141          \item Simulation sequence
 142         \end{itemize}
 143   \item Simulation results
 144         \begin{itemize}
 145          \item Interstitials in silicon
 146          \item SiC-precipitation experiments
 147         \end{itemize}
 148   \item Conclusion / Outlook
 149  \end{itemize}
 150 \end{slide}
 151
 152 % start of contents
 153
 154 \begin{slide}
 155
 156  {\large\bf
 157   Motivation / Introduction
 158  }
 159
 160  \vspace{16pt}
 161
 162  Reasons for investigating C in Si:
 163
 164  \begin{itemize}
 165   \item 3C-SiC wide band gap semiconductor formation
 166   \item Strained Si (no precipitation wanted!)
 167  \end{itemize}
 168
 169  \vspace{16pt}
 170
 171  Si / 3C-SiC facts:
 172
 173  \begin{minipage}{8cm}
 174  \begin{itemize}
 175   \item Unit cell:
 176         \begin{itemize}
 177          \item {\color{yellow}fcc} $+$
 178          \item {\color{gray}fcc shifted $1/4$ of volume diagonal}
 179         \end{itemize}
 180   \item Lattice constants: $4a_{Si}\approx5a_{SiC}$
 181   \item Silicon density:
 182         \[
 183         \frac{n_{SiC}}{n_{Si}}=
 184         \frac{4/a_{SiC}^3}{8/a_{Si}^3}=
 185         \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
 186         \]
 187  \end{itemize}
 188  \end{minipage}
 189  \hspace{8pt}
 190  \begin{minipage}{4cm}
 191  \includegraphics[width=4cm]{sic_unit_cell.eps}
 192  \end{minipage}
 193
 194 \end{slide}
 195
 196  \small
 197 \begin{slide}
 198
 199  {\large\bf
 200   Motivation / Introduction
 201  }
 202
 203  \small
 204  \vspace{6pt}
 205
 206  Supposed conversion mechanism of heavily carbon doped Si into SiC:
 207
 208  \vspace{8pt}
 209
 210  \begin{minipage}{3.8cm}
 211  \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
 212  \end{minipage}
 213  \hspace{0.6cm}
 214  \begin{minipage}{3.8cm}
 215  \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
 216  \end{minipage}
 217  \hspace{0.6cm}
 218  \begin{minipage}{3.8cm}
 219  \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
 220  \end{minipage}
 221
 222  \vspace{8pt}
 223
 224  \begin{minipage}{3.8cm}
 225  Formation of C-Si dumbbells on regular c-Si lattice sites
 226  \end{minipage}
 227  \hspace{0.6cm}
 228  \begin{minipage}{3.8cm}
 229  Agglomeration into large clusters (embryos)\\
 230  \end{minipage}
 231  \hspace{0.6cm}
 232  \begin{minipage}{3.8cm}
 233  Precipitation of 3C-SiC + Creation of interstitials\\
 234  \end{minipage}
 235
 236  \vspace{12pt}
 237
 238  Experimentally observed:
 239  \begin{itemize}
 240   \item Minimal diameter of precipitation: 4 - 5 nm
 241   \item (hkl)-planes identical for Si and SiC
 242  \end{itemize}
 243
 244 \end{slide}
 245
 246 \begin{slide}
 247
 248  {\large\bf
 249   Simulation details
 250  }
 251
 252  \vspace{12pt}
 253
 254  MD basics:
 255  \begin{itemize}
 256   \item Microscopic description of N particle system
 257   \item Analytical interaction potential
 258   \item Hamilton's equations of motion as propagation rule\\
 259         in 6N-dimensional phase space
 260   \item Observables obtained by time average
 261  \end{itemize}
 262
 263  \vspace{12pt}
 264
 265  Application details:
 266  \begin{itemize}
 267   \item Integrator: Velocity Verlet, timestep: $1\, fs$
 268   \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
 269   \item Potential: Tersoff-like bond order potential\\
 270         \[
 271         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 272         \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
 273         \]
 274         \begin{center}
 275         {\scriptsize P. Erhart und K. Albe. Phys. Rev. B 71 (2005) 035211}
 276         \end{center}
 277  \end{itemize}
 278
 279  \begin{picture}(0,0)(-240,-70)
 280   \includegraphics[width=5cm]{tersoff_angle.eps}
 281  \end{picture}
 282
 283 \end{slide}
 284
 285 \begin{slide}
 286
 287  {\large\bf
 288   Simulation details
 289  }
 290
 291  \vspace{20pt}
 292
 293  Interstitial experiments:
 294
 295  \vspace{12pt}
 296
 297  \begin{itemize}
 298   \item Initial configuration: $9\times9\times9$ unit cells Si
 299   \item Periodic boundary conditions
 300   \item $T=0 \, K$
 301   \item Insertion of Si / C atom at
 302         \begin{itemize}
 303          \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
 304          \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
 305          \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
 306                $\rightarrow$ {\color{yellow}110 dumbbell}
 307          \item random positions (critical distance check)
 308         \end{itemize}
 309   \item Relaxation time: $2\, ps$
 310   \item Optional heating-up
 311  \end{itemize}
 312
 313  \begin{picture}(0,0)(-210,-45)
 314   \includegraphics[width=6cm]{unit_cell.eps}
 315  \end{picture}
 316
 317 \end{slide}
 318
 319 \begin{slide}
 320
 321  {\large\bf
 322   Simulation details
 323  }
 324
 325  \small
 326
 327  SiC precipitation experiments:
 328
 329  \begin{pspicture}(0,0)(12,8)
 330   % nodes
 331   \rput(4.5,6.5){\rnode{init}{\psframebox{\parbox{7cm}{
 332    \begin{itemize}
 333     \item Initial configuration: $31\times31\times31$ unit cells Si
 334     \item Periodic boundary conditions
 335     \item $T=450\, ^{\circ}C$
 336     \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
 337    \end{itemize}
 338   }}}}
 339   \rput(4.5,4.5){\rnode{tc1}{\psframebox[fillstyle=solid,fillcolor=red]{
 340                              $T=450\pm 1\, ^{\circ}C$}}}
 341   \rput(7,3.5){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
 342                               \parbox{3cm}{
 343                               Insertion of 10 atoms\\
 344                               at random positions}}}}
 345   \rput(2,3.5){\rnode{adj1}{\psframebox[fillstyle=solid,fillcolor=red]{
 346                             \parbox{3.5cm}{
 347                             Adjusting temperature\\
 348                             for another $100\, fs$}}}}
 349   \rput(7,2.5){\rnode{nc}{\psframebox[fillstyle=solid,fillcolor=red]{
 350                           $N_{atoms}=6000$}}}
 351   \rput(4.5,2){\rnode{tc2}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 352                            $T=T_{set}$}}}
 353   \rput(7,1){\rnode{td}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 354                         $T_{set}:=T_{set}-1\, ^{\circ}C$}}}
 355   \rput(2,1){\rnode{adj2}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 356                           \parbox{3.5cm}{
 357                           Adjusting temperature\\
 358                           for another $50\, fs$}}}}
 359   \rput(7,0){\rnode{tc3}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 360                          $T_{set}=20\, ^{\circ}C$}}}
 361   \rput(10,0){\rnode{end}{\psframebox{End}}}
 362   % help nodes
 363   \rput(7,4.5){\pnode{tc1-h}}
 364   \rput(2,4.5){\pnode{tc1-hh}}
 365   \rput(4.5,2.5){\pnode{nc-h}}
 366   \rput(9,2.5){\pnode{nc-hh}}
 367   \rput(9,2){\pnode{tc2-h}}
 368   \rput(2,2){\pnode{tc2-hh}}
 369   \rput(4.5,0){\pnode{tc3-h}}
 370   % direct lines
 371   \ncline[]{->}{init}{tc1}
 372   \ncline[]{->}{adj1}{tc1}
 373   \ncline[]{->}{insert}{nc}
 374   \ncline[]{->}{adj2}{tc2}
 375   \ncline[]{->}{tc2}{td}
 376   \lput*{0}{yes}
 377   \ncline[]{->}{td}{tc3}
 378   \ncline[]{->}{tc3}{end}
 379   \lput*{0}{yes}
 380   % lines using help nodes
 381   \ncline[]{tc1}{tc1-h}
 382   \lput*{0}{yes}
 383   \ncline[]{->}{tc1-h}{insert}
 384   \ncline[]{tc1}{tc1-hh}
 385   \lput*{0}{no}
 386   \ncline[]{->}{tc1-hh}{adj1}
 387   \ncline[]{nc}{nc-h}
 388   \lput*{0}{no}
 389   \ncline[]{->}{nc-h}{tc1}
 390   \ncline[]{nc}{nc-hh}
 391   \ncline[]{-}{nc-hh}{tc2-h}
 392   \ncline[]{->}{tc2-h}{tc2}
 393   \lput*{0}{yes, {\footnotesize $T_{set}:=450\, ^{\circ}C$}}
 394   \ncline[]{tc2}{tc2-hh}
 395   \lput*{0}{no}
 396   \ncline[]{->}{tc2-hh}{adj2}
 397   \ncline[]{tc3}{tc3-h}
 398   \lput*{0}{no}
 399   \ncline[]{->}{tc3-h}{tc2}
 400   % insertion volumes
 401   \psframe[fillstyle=solid,fillcolor=white](9.5,1.3)(13.5,5.3)
 402   \psframe[fillstyle=solid,fillcolor=lightgray](10,1.8)(13,4.8)
 403   \psframe[fillstyle=solid,fillcolor=gray](10.5,2.3)(12.5,4.3)
 404   \rput(9.75,3){\pnode{ins1}}
 405   \rput(10.25,3.3){\pnode{ins2}}
 406   \rput(10.75,3.6){\pnode{ins3}}
 407   \ncline[]{-}{insert}{ins1}
 408   \ncline[]{-}{insert}{ins2}
 409   \ncline[]{-}{insert}{ins3}
 410   \psframe[fillstyle=solid,fillcolor=white](9.5,7.6)(13.5,8.1)
 411   \psframe[fillstyle=solid,fillcolor=lightgray](9.5,6.8)(13.5,7.3)
 412   \psframe[fillstyle=solid,fillcolor=gray](9.5,6)(13.5,6.5)
 413   \rput(11.5,7.85){{\tiny Simulation volume:
 414                           $31\times31\times31\, a^3_{Si}$}}
 415   \rput(11.5,7.05){{\tiny Volume of minimal SiC precipitation}}
 416   \rput(11.5,6.25){{\tiny Volume of necessary amount of Si}}
 417  \end{pspicture}
 418
 419 \end{slide}
 420
 421 \begin{slide}
 422
 423  {\large\bf
 424   Results
 425  }
 426
 427  Si self-interstitial experiments:
 428
 429  {\footnotesize
 430  {\bf Note:}
 431  \begin{itemize}
 432   \item $r_{cutoff}^{Si-Si}=2.96>\frac{5.43}{2}$
 433   \item Bond length near $r_{cutoff} \Rightarrow$ small bond strength
 434  \end{itemize}
 435  }
 436
 437  \vspace{8pt}
 438
 439  \small
 440
 441  \begin{minipage}[t]{4.0cm}
 442  \underline{Tetrahedral}
 443  \begin{itemize}
 444   \item $E_f=3.41\, eV$
 445   \item essentialy tetrahedral\\
 446         bonds
 447  \end{itemize}
 448  \end{minipage}
 449  \hspace{0.3cm}
 450  \begin{minipage}[t]{4.0cm}
 451  \underline{110 dumbbell}
 452  \begin{itemize}
 453   \item $E_f=4.39\, eV$
 454   \item essentially 4 bonds
 455  \end{itemize}
 456  \end{minipage}
 457  \hspace{0.3cm}
 458  \begin{minipage}[t]{4.0cm}
 459  \underline{Hexagonal}
 460  \begin{itemize}
 461   \item $E_f^{\star}\approx4.48\, eV$
 462   \item unstable!
 463  \end{itemize}
 464  \end{minipage}
 465
 466  \vspace{8pt}
 467
 468  \begin{minipage}{4.3cm}
 469  \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
 470  \end{minipage}
 471  \begin{minipage}{4.3cm}
 472  \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
 473  \end{minipage}
 474  \begin{minipage}{4.3cm}
 475  \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
 476  \end{minipage}
 477
 478 \end{slide}
 479
 480 \begin{slide}
 481
 482  {\large\bf
 483   Results
 484  }
 485
 486  \vspace{8pt}
 487
 488  Si self-interstitial \underline{random insertion} experiments:
 489
 490  \vspace{8pt}
 491
 492  foo
 493
 494 \end{slide}
 495
 496 \begin{slide}
 497
 498  {\large\bf
 499   Results
 500  }
 501
 502  Carbon interstitial experiments:
 503
 504  \vspace{8pt}
 505
 506  \small
 507
 508  \begin{minipage}[t]{4.0cm}
 509  \underline{Tetrahedral}
 510  \begin{itemize}
 511   \item $E_F=2.67\, eV$
 512   \item tetrahedral bond
 513  \end{itemize}
 514  \end{minipage}
 515  \hspace{0.3cm}
 516  \begin{minipage}[t]{4.0cm}
 517  \underline{110 dumbbell}
 518  \begin{itemize}
 519   \item $E_F=1.76\, eV$
 520   \item C forms 3 bonds
 521  \end{itemize}
 522  \end{minipage}
 523  \hspace{0.3cm}
 524  \begin{minipage}[t]{4.0cm}
 525  \underline{Hexagonal}
 526  \begin{itemize}
 527   \item $E_F^{\star}\approx5.6\, eV$
 528   \item unstable!
 529  \end{itemize}
 530  \end{minipage}
 531
 532  \vspace{8pt}
 533
 534  \begin{minipage}{4.3cm}
 535  \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
 536  \end{minipage}
 537  \begin{minipage}{4.3cm}
 538  \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
 539  \end{minipage}
 540  \begin{minipage}{4.3cm}
 541  \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
 542  \end{minipage}
 543
 544 \end{slide}
 545
 546 \begin{slide}
 547
 548  {\large\bf
 549   Results
 550  }
 551
 552  \vspace{8pt}
 553
 554  Carbon \underline{random insertion} experiments:
 555
 556  \vspace{8pt}
 557
 558  bar
 559
 560 \end{slide}
 561
 562 \begin{slide}
 563
 564  {\large\bf
 565   Results
 566  }
 567
 568  SiC-precipitation experiments:
 569
 570 \end{slide}
 571
 572 \begin{slide}
 573
 574  {\large\bf
 575   Conclusion / Outlook
 576  }
 577
 578 \end{slide}
 579
 580 \end{document}
 581